Statistica Sinica 15(2005), 871-888

TWO-STAGE GROUP SCREENING IN THE PRESENCE OF

NOISE FACTORS AND UNEQUAL PROBABILITIES OF

ACTIVE EFFECTS

A. E. Vine$^1$, S. M. Lewis$^1$ and A. M. Dean$^2$

$^1$University of Southampton and $^2$Ohio State University

Abstract: Group screening is a technique for examining a large number of factors in order to discover the few factors that have important influences on a measured response. In two-stage group screening, factors are assigned to groups and new ``grouped factors'' are investigated in a first stage experiment by varying all the factor values within a group simultaneously. The factors within those groups identified as important are then investigated individually in a second stage experiment. This paper describes theory and software that allows investigation of group screening in the presence of unequal-sized groups of factors in the first stage experiment and different probabilities of the various main effects and interactions being important (or active). Examples are given to show how the results can be used in practice to guide the choice of the number and sizes of the groups and to investigate the advantages and disadvantages of different group screening strategies.

Key words and phrases: Design of experiments, fractional factorial experiment, interaction, noise factor, screening, simulation.